We consider Big Data as a phenomenon with acquired properties, similar to collective behaviours, that establishes virtual collective beings. We consider the occurrence of ongoing non-equivalent multiple properties in the conceptual framework of structural dynamics given by sequences of structures and not only by different values assumed by the same structure. We consider the difference between modelling and profiling in a constructivist way, as De Finetti intended probability to exist, depending on the configuration taken into consideration. The past has little or no influence, while events and their configurations are not memorised. Any configuration of events is new, and the probabilistic values to be considered are reset. As for collective behaviours, we introduce methodological and conceptual proposals using mesoscopic variables and their property profiles and meta-profile Big Data and non-computable profiles which were inspired by the use of natural computing to deal with cyber-ecosystems. The focus is on ongoing profiles, in which the arising properties trace trajectories, rather than assuming that we can foresee them based on the past.We assume that dealing with Big Data as a phenomenon contains not only traces of past events, but also the assumption of having properties that are independent from the original event, when studied as a virtual collective being [6]. Thus, we consider the occurrence of ongoing, non-equivalent, multiple properties with any initial temporal beginning, duration, and variable combination in conceptual correspondence with the nature of quasi-systems, which occur when a system is not always the same system and or even a system at all [7,8].We then mention the criticality of the level of description, as well as the scalarity assumed to detect the properties as well as the conceptual ineffectiveness of increasing the quantity of data available. Before proposing new approaches allowed by the conceptual 'definitions' mentioned above, we consider the differences between models and profiles. Models (especially ideal) are expected to support understanding, while profiling is intended to represent non-ideal, data-driven models, and their emergent, ongoing properties, for example, correlations and coherences [9]. Another differentiation considered is between forecasting and understanding. Forecasting is based on the importance of the past, is based on analogies and repetitiveness, and takes some contextual conditions into account. Understanding is considered to be the ability to conjecture, hypothesise, speculate, and, finally, realise the nature of the phenomenon under study, for instance, chaotic, hosting bifurcations, fluctuations, and the presence of multiple dynamic coherences.We specify that the differences introduced above should be considered in a constructivist conceptual framework in which, instead of trying to find how a phenomenon 'really' is, one looks for the most effective way to think of it (multiple modelling) [10]. For instance, we consider the conceptual framework of the t...